Numeric Data Types

Overview

Teaching: 5 min
Exercises: 0 min

Questions

• What kinds of data do programs store?

• How can I convert one type to another?

Objectives

• Explain key differences between integers and floating point numbers.

• Explain key differences between numbers and character strings.

• Use built-in functions to convert between integers, floating point numbers, and strings.

Every value has a type.

• Every value in a program has a specific type.
• Integer (int): counting numbers like 3 or -512.
• Floating point number (float): fractional numbers like 3.14159 or -2.5.
  • Integers are used to count, floats are used to measure.
• Character string (usually called “string”, str): text.
  • Written in either single quotes or double quotes (as long as they match).
  • The quotation marks aren’t printed when the string is displayed.

Use the built-in function type to find the type of a value.

• Use the built-in function type to find out what type a value has.
• Works on variables as well.
  • But remember: the value has the type — the variable is just a label.

print(type(52))

<class 'int'>

fitness = 'average'
print(type(fitness))

<class 'str'>

Types control what operations (or methods) can be performed on a given value.

• A value’s type determines what the program can do to it.

print(5 - 3)

2

print('hello' - 'h')

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-2-67f5626a1e07> in <module>()
----> 1 print('hello' - 'h')

TypeError: unsupported operand type(s) for -: 'str' and 'str'

Can mix integers and floats freely in operations.

• Integers and floating-point numbers can be mixed in arithmetic.
  • Python automatically converts integers to floats as needed.

print('half is', 1 / 2.0)
print('three squared is', 3.0 ** 2)

half is 0.5
three squared is 9.0

Must convert numbers to strings or vice versa when operating on them.

• Cannot add numbers and strings.

print(1 + 'A')

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-4-fe4f54a023c6> in <module>()
----> 1 print(1 + '2')

TypeError: unsupported operand type(s) for +: 'int' and 'str'

• Not allowed because it’s ambiguous: should 1 + '2' be 3 or '12'?
• Some types can be converted to other types by using the type name as a function.

print(1 + int('2'))
print(str(1) + '2')

3
12

Variables only change value when something is assigned to them.

• If we make one cell in a spreadsheet depend on another, and update the latter, the former updates automatically.
• This does not happen in programming languages.

first = 1
second = 5 * first
first = 2
print('first is', first, 'and second is', second)

first is 2 and second is 5

• The computer reads the value of first when doing the multiplication, creates a new value, and assigns it to second.
• After that, second does not remember where it came from.

Fractions

What type of value is 3.4? How can you find out?

Solution

It is a floating-point number (often abbreviated “float”).

print(type(3.4))

<class 'float'>

Automatic Type Conversion

What type of value is 3.25 + 4?

Solution

It is a float: integers are automatically converted to floats as necessary.

result = 3.25 + 4
print(result, 'is', type(result))

7.25 is <class 'float'>

Choose a Type

What type of value (integer, floating point number, or character string) would you use to represent each of the following? Try to come up with more than one good answer for each problem. For example, in # 1, when would counting days with a floating point variable make more sense than using an integer?

1. Number of days since the start of the year.
2. Time elapsed since the start of the year.
3. Serial number of a piece of lab equipment.
4. A lab specimen’s age.
5. Current population of a city.
6. Average population of a city over time.

Division Types

In Python 3, the // operator performs integer (whole-number) floor division, the / operator performs floating-point division, and the ‘%’ (or modulo) operator calculates and returns the remainder from integer division:

print('5 // 3:', 5//3)
print('5 / 3:', 5/3)
print('5 % 3:', 5%3)

5 // 3: 1
5 / 3: 1.6666666666666667
5 % 3: 2

However in Python2 (and other languages), the / operator between two integer types perform a floor (//) division. To perform a float division, we have to convert one of the integers to float.

print('5 // 3:', 1)
print('5 / 3:', 1 )
print('5 / float(3):', 1.6666667 )
print('float(5) / 3:', 1.6666667 )
print('float(5 / 3):', 1.0 )
print('5 % 3:', 2)

If num_subjects is the number of subjects taking part in a study, and num_per_survey is the number that can take part in a single survey, write an expression that calculates the number of surveys needed to reach everyone once.

Solution

Depending on requirements it might be important to detect when the number of subjects per survey doesn’t divide the number of subjects evenly. Detect it with the % operator and test if the remainder that it returns is greater than 0.

num_subjects = 600
num_per_survey = 42
num_surveys = num_subjects // num_per_survey
remainder = num_subjects % num_per_survey

print(num_subjects, 'subjects,', num_per_survey, 'per survey:', num_surveys)

600 subjects, 42 per survey: 14

Strings to Numbers

Where reasonable, float() will convert a string to a floating point number, and int() will convert a floating point number to an integer:

print("string to float:", float("3.4"))
print("float to int:", int(3.4))

string to float: 3.4
float to int: 3

If the conversion doesn’t make sense, however, an error message will occur

print("string to float:", float("Hello world!"))

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-5-df3b790bf0a2> in <module>()
----> 1 print("string to float:", float("Hello world!"))

ValueError: could not convert string to float: 'Hello world!'

Given this information, what do you expect the following program to do?

What does it actually do?

Why do you think it does that?

print("fractional string to int:", int("3.4"))

Solution

What do you expect this program to do? It would not be so unreasonable to expect the Python 3 int command to convert the string “3.4” to 3.4 and an additional type conversion to 3. After all, Python 3 performs a lot of other magic - isn’t that part of its charm?

However, Python 3 throws an error. Why? To be consistent, possibly. If you ask Python to perform two consecutive typecasts, you must convert it explicitly in code.

int("3.4")
int(float("3.4"))

In [2]: int("3.4")
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-2-ec6729dfccdc> in <module>()
----> 1 int("3.4")
ValueError: invalid literal for int() with base 10: '3.4'
3

Arithmetic with Different Types

Which of the following will print 2.0? Note: there may be more than one right answer.

first = 1.0
second = "1"
third = "1.1"

1. first + float(second)
2. float(second) + float(third)
3. first + int(third)
4. first + int(float(third))
5. int(first) + int(float(third))
6. 2.0 * second

Solution

Answer: 1 and 4

Complex Numbers

Python provides complex numbers, which are written as 1.0+2.0j. If val is an imaginary number, its real and imaginary parts can be accessed using dot notation as val.real and val.imag.

1. Why do you think Python uses j instead of i for the imaginary part?
2. What do you expect 1+2j + 3 to produce?
3. What do you expect ‘4j’ to be? What about 4 j or `4 + j’? >

Solution

1. Standard mathematics treatments typically use i to denote an imaginary number. However, from media reports it was an early convention established from electrical engineering that now presents a technically expensive area to change. Stack Overflow provides additional explanation and discussion
2. 4+2j
3. 4j, syntax error, depends on the value of j

Key Points

• Every value has a type.

• Use the built-in function type to find the type of a value.

• Types control what operations can be done on values.

• Strings can be added and multiplied.

• Strings have a length (but numbers don’t).

• Must convert numbers to strings or vice versa when operating on them.

• Can mix integers and floats freely in operations.

• Variables only change value when something is assigned to them.